Open
Description
Task 8: Case Study Development
Problem
No real-world examples demonstrating RFH3 effectiveness.
Implementation Plan
Create comprehensive case studies with real historical data and systematic analysis:
Case Study Notebooks:
1. 08_case_studies/01_rsa_challenge_numbers.ipynb
- Historical RSA Challenges: Analysis of RSA-100, RSA-129, RSA-155, RSA-768
- Timeline Comparisons: Historical factorization time vs RFH3 projections
- Security Impact Analysis: Implications for current cryptographic systems
- Future Challenge Predictions: Projected timeline for remaining RSA challenges
class RSAChallengeAnalyzer:
def __init__(self):
self.rsa_challenges = {
'RSA-100': {
'number': '1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139',
'bits': 330,
'factored_year': 1991,
'factoring_time': '17 days',
'method': 'Quadratic Sieve'
},
'RSA-129': {
'number': '114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541',
'bits': 426,
'factored_year': 1994,
'factoring_time': '8 months',
'method': 'Quadratic Sieve'
}
# ... more challenges
}
def analyze_historical_performance(self, challenge_name: str):
"""Compare historical vs RFH3 projected performance"""
# RFH3 time estimate
# Resource requirement analysis
# Success probability calculation
# Security timeline projection
pass
def project_future_challenges(self):
"""Predict timeline for remaining challenges"""
# RFH3 capability growth modeling
# Hardware improvement projections
# Algorithm advancement estimates
# Risk assessment for each challenge
pass2. 08_case_studies/02_balanced_vs_unbalanced_semiprimes.ipynb
- Systematic Performance Analysis: Performance across different semiprime balance ratios
- Phase Effectiveness Study: Which phases work best for different semiprime types
- Pattern Recognition: Learning patterns specific to balanced/unbalanced cases
- Optimization Strategies: Tailored approaches for different semiprime structures
class SemiprimeTypeAnalyzer:
def categorize_semiprime_balance(self, p: int, q: int) -> str:
"""Categorize semiprime by factor balance"""
ratio = max(p, q) / min(p, q)
if ratio < 1.1:
return 'highly_balanced'
elif ratio < 2.0:
return 'moderately_balanced'
elif ratio < 10.0:
return 'moderately_unbalanced'
else:
return 'highly_unbalanced'
def analyze_phase_effectiveness(self, semiprime_type: str, test_cases: list):
"""Analyze which phases work best for semiprime type"""
# Phase 0: Small prime effectiveness
# Phase 1: Balanced search effectiveness
# Phase 2: Hierarchical search effectiveness
# Phase 3: Adaptive resonance effectiveness
# Phase 4: Advanced algorithm effectiveness
pass
def identify_optimization_opportunities(self, analysis_results: dict):
"""Identify optimization strategies for each type"""
# Parameter tuning recommendations
# Phase timeout adjustments
# Algorithm selection strategies
# Learning pattern adaptations
pass3. 08_case_studies/03_failure_analysis_and_learning.ipynb
- Systematic Failure Analysis: When and why RFH3 fails
- Failure Mode Classification: Different types of failure patterns
- Learning from Failures: How the system improves from failed attempts
- Mitigation Strategies: Approaches to reduce failure rates
class FailureAnalyzer:
def classify_failure_mode(self, factorization_attempt: dict) -> str:
"""Classify the type of failure"""
# Timeout failures
# Resonance field navigation failures
# Memory/resource failures
# Algorithm convergence failures
# Edge case failures
pass
def analyze_failure_patterns(self, failure_log: list):
"""Identify patterns in failures"""
# Number size correlation
# Factor structure correlation
# Algorithm phase correlation
# Resource constraint correlation
pass
def evaluate_learning_effectiveness(self, before_after_data: dict):
"""Measure improvement after learning from failures"""
# Success rate improvement
# Time to solution improvement
# Resource efficiency improvement
# Pattern recognition accuracy
pass4. 08_case_studies/04_scaling_behavior_analysis.ipynb
- Empirical Scaling Analysis: How performance scales with bit length
- Resource Usage Scaling: Memory and CPU requirements vs problem size
- Success Rate Scaling: How success rate changes with number size
- Theoretical vs Empirical: Comparison with theoretical predictions
class ScalingAnalyzer:
def measure_time_complexity(self, bit_sizes: list, sample_sizes: list):
"""Empirical time complexity measurement"""
# Generate test cases for each bit size
# Measure factorization times
# Fit complexity models
# Compare with theoretical predictions
pass
def measure_space_complexity(self, bit_sizes: list):
"""Empirical space complexity measurement"""
# Memory usage profiling
# Cache size requirements
# Working set analysis
# Scalability bottlenecks
pass
def analyze_success_rate_scaling(self, performance_data: dict):
"""Analyze how success rate changes with scale"""
# Success rate by bit size
# Failure mode distribution
# Phase effectiveness scaling
# Learning curve analysis
passInteractive Analysis Tools:
Performance Comparison Dashboard:
- Historical vs RFH3 performance visualization
- Interactive timeline projections
- Security impact assessment tools
- Risk analysis calculators
Semiprime Type Explorer:
- Interactive semiprime generation and classification
- Real-time performance prediction
- Optimization recommendation engine
- Comparative analysis tools
Failure Pattern Visualizer:
- Failure mode distribution charts
- Pattern correlation heatmaps
- Learning effectiveness tracking
- Mitigation strategy recommendations
Scaling Behavior Plots:
- Log-log scaling plots with confidence intervals
- Resource usage projections
- Performance envelope analysis
- Theoretical vs empirical comparisons
Real-World Data Integration:
Historical Datasets:
- RSA challenge factorization records
- Academic benchmark results
- Cryptographic competition data
- Performance benchmarking studies
Live Data Sources:
- Current factorization challenges
- Hardware performance trends
- Algorithm advancement tracking
- Security vulnerability reports
Validation Data:
- Independent verification of results
- Cross-validation with other tools
- Reproducibility confirmation
- External benchmark comparisons
Professional Analysis Standards:
Statistical Rigor:
- Confidence intervals for all measurements
- Statistical significance testing
- Multiple hypothesis correction
- Effect size reporting
Reproducibility:
- Complete methodology documentation
- Seed and environment specification
- Data provenance tracking
- Result verification procedures
Industry Standards:
- Cryptographic security evaluation standards
- Performance benchmarking protocols
- Risk assessment methodologies
- Regulatory compliance considerations
Acceptance Criteria
- Real historical data and comparisons
- Systematic performance analysis across number types
- Failure mode identification and mitigation
- Scaling behavior validation with data
- Professional-quality case study reports
- Interactive analysis tools functional
- Statistical rigor in all analyses
- Reproducible results with proper documentation
Files to Create
notebooks/
├── 08_case_studies/
│ ├── 01_rsa_challenge_numbers.ipynb
│ ├── 02_balanced_vs_unbalanced_semiprimes.ipynb
│ ├── 03_failure_analysis_and_learning.ipynb
│ └── 04_scaling_behavior_analysis.ipynb
├── data/
│ ├── rsa_challenges/
│ │ ├── challenge_database.json
│ │ ├── historical_performance.csv
│ │ └── security_timeline.json
│ ├── semiprime_datasets/
│ │ ├── balanced_semiprimes.json
│ │ ├── unbalanced_semiprimes.json
│ │ └── performance_by_type.csv
│ ├── failure_analysis/
│ │ ├── failure_logs.json
│ │ ├── pattern_analysis.csv
│ │ └── learning_curves.json
│ └── scaling_studies/
│ ├── performance_measurements.csv
│ ├── resource_usage.json
│ └── theoretical_predictions.json
└── shared/
└── case_studies/
├── rsa_analyzer.py
├── semiprime_analyzer.py
├── failure_analyzer.py
├── scaling_analyzer.py
└── report_generator.py
Implementation Notes
- Use real RSA challenge data with proper attribution
- Include confidence intervals and statistical significance
- Provide interactive widgets for parameter exploration
- Generate publication-ready figures and tables
- Include regulatory and compliance considerations
- Support export to multiple report formats
- Integrate with external benchmarking tools
- Maintain data provenance and version control